Which functions are increasing over the domain

y=(1/2)^x
y=10^x
y=4^x


http://my.hrw.com/math06_07/nsmedia/tool…

For the function(s) that are increasing over the domain, is the “a” value > or < 1?
For the function(s) that are decreasing over the domain, is the “a” value > or < 1?

I dont really understand this question..

(A) Which functions are increasing over the domain?

To see if y=(1/2)^x is increasing or decreasing, we can make a table:
x | y
---|---
0 | (1/2)^0 = 1
1 | (1/2)^1 = 1/2
2 | (1/2)^2 = 1/4
3 | (1/2)^3 = 1/8

As x increases in value, y decreases in value, so the function is decreasing.
(You can also look at the graph and see that as you follow the graph from left to right, the graph goes down, or decreases.)

To see if y=(10)^x is increasing or decreasing, we can make a table:
x | y
---|---
0 | (10)^0 = 1
1 | (10)^1 = 10
2 | (10)^2 = 100
3 | (10)^3 = 1000

As x increases in value, y also increases in value, so the function is increasing. (If you follow the graph from left to right, you can see that it goes up, or increases.)

Do the same for the other function.


(B) For the function(s) that are increasing over the domain, is the “a” value > or < 1?
For the function(s) that are decreasing over the domain, is the “a” value > or < 1?

These functions are all exponential in the form f(x) = a^x
For y=(1/2)^x, the “a” value is 1/2 which is <1. We saw earlier that this function is decreasing.
For y=10^x, the “a” value is 10 which is >1. Based on our earlier answer, is this function increasing or decreasing?
What happens for the third function?

So far, we see that for the decreasing function, the value of “a” is less than 1. Now figure out what happens when the value of “a” is more than 1.

These are exponential functions
This kind of functions are increasing if a (the base is >1 and decreasing if a <1
so the first is decreasing and the second and third are increasing